The 21-year-old English midfielder, who joined Swansea from Liverpool in July, gave Swansea a second-minute lead in Monday's game at the Liberty Stadium. He quickly undid his hard work, however, with a dreadful back-pass, allowing Daniel Sturridge to equalise 99 seconds later, before another loose pass saw Victor Moses put Liverpool ahead. The former Charlton Athletic midfielder managed to atone though, teeing up Michu for a 64th-minute equaliser with a deft header.
Shelvey apologised to Swansea's supporters in a post-match television interview, but Laudrup said he had no reason to say sorry.
"He had no need to do that," said the Dane. "Nobody makes mistakes on purpose, but it shows how he is.
"The most important thing was his reaction. It's difficult after a first half like that. You feel you could have done better, but I said there were 45 more minutes and we dominated the last 25 minutes of the game."
"It was a difficult first half for him. But I said, 'There is no problem. Go out there, you still have 45 minutes to turn it around.'
"He knew only he could bring himself back into the game and it was a fantastic reaction to pull himself together. It says a lot about him. He is still very young and he will be stronger for this game."
Rodgers praises Shelvey, Sturridge
Liverpool manager Brendan Rodgers also praised his former player's reaction.
"He kept going, bless him," said the Northern Irishman. "He is a terrific boy who made a brave decision to leave a club like Liverpool, and nights like this are why he left to learn.
"He took his goal well but when you play against good players they can punish you, and Sturridge is lethal and will be one of the top strikers in Europe over the next few years. But Jonjo will prove to be a very good player."
It was the first time Liverpool had dropped points in the league this season, but they nonetheless returned to the top of the table. It came at a cost, however, as Brazilian playmaker Philippe Coutinho was forced off with a shoulder injury in the second half.
Swansea, meanwhile, will probably be without Spanish midfielder Pablo Hernandez for this week's games against Valencia and Crystal Palace due to a hamstring injury.